Preheat the over to 350 degrees F.
In a small saucepan, warm the milk and 2 teaspoons of the butter together over medium-low heat. With an electric mixer fitted with a wire whip, beat the eggs and 1 cup of the sugar on medium-high speed in a large mixing bowl until the mixture is pale yellow, thick, and tripled in volume, about 8 minutes. With the mixer on low speed, beat in the warm milk mixture. Sift the flour, cocoa, baking powder, and salt into a small mixing bowl. Add half the flour mixture to the egg mixture and blend thoroughly until smooth.
Repeat with the other half. Add the vanilla and mix gently. Grease a 17 x 12 inch baking pan or jellyroll pan with the remaining 2 tablespoons butter. Sprinkle evenly with the remaining 2 tablespoons sugar. Pour the cake batter into the pan, spreading it evenly. Bake until the cake springs back when touched, about 15 minutes. Cool for about 2 minutes, then gently flip it out onto a large sheet of parchment paper. Let cool completely.
FOR THE FILLING:
Combine the sugar and water in a small saucepan over medium heat. Bring to a boil, stirring to dissolve the sugar, and cook for 2 minutes. Remove from the heat and let cool completely. Stir in 1 cup of the kirsch and stir to mix.
In another saucepan over medium heat, bring the cherries to a boil in their syrup. In a small bowl, dissolve the cornstarch in the remaining 1/4 cup kirsch and add to the cherry mixture. Whisk until it thickens, about 2 minutes. Remove from the heat and cool completely.
ASSEMBLE THE CAKE:
Using a serrated knife, carefully cut each cake horizontally in half to make four layers. Brush the tops of all the layers with equal amounts of the sugar syrup. Let the liquid soak into the layers for about 30 minutes. Place the bottom layer on a large cake plate. Spread 1 cup of the filling evenly over this layer, then top with a second layer of cake. Spread 1 cup of the filling evenly over it. Repeat the same process with the third layer and another cup of the filling. Top with the fourth layer.
Sift together the confectioners' sugar and cocoa powder into a medium size bowl. Add the butter and mix with an electric mixer until incorporated. Add 1 teaspoon of the vanilla and the boiling water and mix until smooth. Let cool. Combine the cream, the remaining 1/2 teaspoon vanilla, and the sugar in a medium-size mixing bowl and, using an electric mixer, whip until soft peaks form. Ice the sides and top of the cake evenly with the chocolate frosting. Spoon the whipped cream over the top of the cake and sprinkle with the chocolate shavings. Slice and serve the cake.